A polyline is a geometric shape composed of line segments. Each line segment in a polyline generally has an endpoint in common with another line segment in the polyline, thereby forming a vertex of the polyline, although this is not true in the case of a polyline that is not a closed polygon. In that case, an endpoint of each of two line segments is an endpoint of the polyline. In any event, polylines often occur in applications that display graphical images. To take just one example, mapping applications often use polylines. Such polylines often have many vertices, and are computationally expensive to process and display. It is therefore often desirable to reduce the number of vertices in a polyline when rendering the polyline. Unfortunately, present systems and methods for efficiently processing and rendering polylines are lacking.